integravimas

Integravimas is a Lithuanian term that refers to the mathematical process of integration, a fundamental operation in calculus. It involves finding an antiderivative of a function or computing the definite integral that represents the accumulated area under a curve between two limits. The concept is central to many areas of science and engineering, providing a means to calculate quantities such as displacement from velocity, work from force, and charge from current.

The theory of integration originated with the work of Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century, who independently formulated the fundamental theorem of calculus. This theorem links the operations of differentiation and integration, establishing that the definite integral can be evaluated using antiderivatives. Later mathematicians, including Joseph Fourier and Augustin-Louis Cauchy, refined the rigorous foundations of integration, giving rise to various integration techniques such as substitution, integration by parts, partial fractions, and trigonometric substitution.

In practical applications, integration is employed in physics to determine quantities like center of mass and electric potential, in engineering for signal processing and control systems, and in economics for calculating consumer surplus and investment growth. Numerical methods such as the trapezoidal rule, Simpson’s rule, and Gaussian quadrature are used when analytic solutions are infeasible.

Overall, integravimas remains a cornerstone of mathematical analysis, enabling the translation of rates of change into cumulative effects across diverse disciplines.